A two-dimensional random variable is a mapping of the points in the sample space to ordered pairs {x, y}. Usually, when dealing with a pair of random variables, the sample space naturally partitions itself so that it can be viewed as a combination of two simpler sample spaces.

Especially in discrete cases, a random variable is sometimes said to be indexed by the domain of its defining function, leading to notations such as X[n]{\displaystyle X[n]} and Xi{\displaystyle X_{i}} to represent particular values of the codomain.